Mass and Width Calculation of $\Lambda(1405)$ and investigation of Mass Spectrum of $\Lambda\longrightarrow(\Sigma\pi)^0$ reaction using Hemigway data
Abstract:
When a negatively charged particle, other than an electron, like muon, pion orbits a nucleus, under a condition in which the principal interaction with the nucleus is electromagnetic, exotic atoms are formed. Exotic atoms formed with the muon are subject to weak interaction, while for all other exotic atoms strong interaction is involved in addition to the electromagnetic interaction with the nucleus. The electromagnetic interaction with the nucleus is very well known, therefore, even a small deviation from the electromagnetic value e.g. due to strong interaction, could be measured performing precision experiments. Studies of exotic (hadronic) atoms have provided important information on strong interaction physics. One of the most important exotic atoms are Kanonic hydrogen atoms. By entering the negative kaon as a hadron in hydrogen and collision with proton, according to strong interaction between meson and baryon, a quasi bound state is formed with the mass of $1405MeV/c^2$ called $\Lambda(1405) \equiv \Lambda^* $.
In this thesis to solve the current debate on the position of the quasi-bound $K^-p$ state, namely $\Lambda(1405)$ or $\Lambda^*$ we have used the data obtained from $K^- $ absorbtion in the bubble chamber of liquid hydrogen. The $\Sigma\pi$ invariant-mass spectra in the resonant capture of $K^-$ at $4.2 GeV/c$ in proton are calculated by a coupled-channel procedure for a $K^-p$ quasi-bound state of an arbitary chosen mass (M) and width $(\Gamma)$. We use the transition matrix and optical phenomenological potential to solve our problem. A $\chi^2$ analysis yielded $M=1405^{+4}_{-3} MeV/c^2$ and $\Gamma=72^{+3}_{-4.2} MeV$. calculation and investigation of the invariant mass spectra of $\Sigma^+ \pi^-$ give a helpful approach to find out the structure of this resonant state. Using $\chi^2$ fitting method experimental data (CERN 2m hydrogrn bubble chamber) are compared to our theoretical results.
{Keywords:}
Exotic atom, Kaonic nuclei,$ \Lambda(1405)$ resonance, Hemingway Data, Invariant mass spectrum.
